Journal of The Electrochemical Society, 154 共12兲 B1378-B1388 共2007兲
B1378
0013-4651/2007/154共12兲/B1378/11/$20.00 © The Electrochemical Society
Interpretation of Low-Frequency Inductive Loops in PEM Fuel Cells Sunil K. Roy,a,* Mark E. Orazem,a,**,z and Bernard Tribolletb,*** a
Department of Chemical Engineering, University of Florida, Gainesville, Florida 32611, USA UPR 15 du CNRS, Laboratoire Interfaces et Systèmes Electrochimiques, Université Pierre et Marie Curie, 75252 Paris, France
b
Impedance models were developed to account for reaction mechanisms that may be responsible for the inductive impedance response often seen at low frequencies in proton exchange membrane 共PEM兲 fuel cells. Models that incorporate reactions without surface intermediates cannot account for these inductive features. Inductive loops can be predicted by models that account for formation of hydrogen peroxide as an intermediate in a two-step oxygen reduction reaction. Hydrogen peroxide is considered to be a degrading agent for materials used in the fuel cell components 共membrane, electrodes兲, and its formation under the fuel cell operating conditions is reported in the literature. Inductive loops can also be predicted by models that account for Pt dissolution and associated deactivation of catalytic activity. These interpretations are supported by experimental evidence reported in the literature. Interpretation of impedance spectra in terms of side reactions may prove useful for predicting the lifetime of fuel cell performance. © 2007 The Electrochemical Society. 关DOI: 10.1149/1.2789377兴 All rights reserved. Manuscript submitted May 30, 2007; revised manuscript received August 16, 2007. Available electronically October 23, 2007.
Impedance spectroscopy is often used to characterize processes in fuel cells, including proton exchange membrane 共PEM兲 fuel cells 共PEMFC兲.1-5 Low-frequency inductive features6-8 are commonly seen in impedance spectra for PEM fuel cells. Makharia et al.6 suggested that side reactions and intermediates involved in the fuel cell operation can be possible causes of the inductive loop seen at low frequency. However, such low-frequency inductive loops could also be attributed to nonstationary behavior, or, due to the time required to make measurements at low frequencies, nonstationary behavior could influence the shapes of the low-frequency features. In previous work, Roy and Orazem9 used the measurement model approach developed by Agarwal et al.10-13 to demonstrate that, for the fuel cell under steady-state operation, the low-frequency inductive loops were consistent with the Kramers–Kronig relations. This work demonstrated that, independent of the instrumentation used, the lowfrequency features could be consistent with the Kramers–Kronig relations. Therefore, the low-frequency inductive loops could be attributed to process characteristics and not to nonstationary artifacts. Some typical results are presented in Fig. 1 for the impedance response of a single 5 cm2 PEMFC with hydrogen and air as reactants. The experimental conditions are reported elsewhere.9 The result presented as Fig. 1a was obtained using a Scribner 850C fuel cell test station and the results presented as Fig. 1b were obtained using a Gamry FC350 impedance instrument coupled with a Dynaload RBL:100V-60A-400W electronic load. The arrow points to the nominal zero-frequency impedance calculated from the slope of the polarization curve, and the solid lines correspond to a fit of the measurement model. Mathematical models are needed to interpret the impedance data, including the low-frequency inductive loops, in terms of physical processes. The most quantitative of the impedance models reported in the literature have emphasized detailed treatment of the transport processes, but use of simple electrochemical mechanisms precluded prediction of the inductive loops. As the oxygen reduction reaction 共ORR兲 at the cathode is the rate-determining step, most models emphasize the reaction kinetics at the cathode. The one-dimensional models proposed by Springer et al.2,14 considered the cathode to be a thin film on agglomerated catalyst particles. They studied the role of water accumulation in the gas diffusion layer and oxygen diffusion in the gas phase. These models considered only a single-step
* Electrochemical Society Student Member. ** Electrochemical Society Fellow. *** Electrochemical Society Active Member. z
E-mail:
[email protected]
irreversible ORR at the cathode. The impedance models by other researchers15-17 also treated a single step kinetics for the ORR. Several models for the impedance response of PEM fuel cells have considered a more detailed reaction mechanism. The model developed by Eikerling and Kornyshev18 considered a single-step ORR to be reversible at the cathode. Antoine et al.7 have proposed an impedance model with a three-step ORR kinetics in acidic medium on platinum nanoparticles though reaction intermediates were unspecified and kinetics at the anode were not considered in their model. They explained that the low-frequency inductive loops were a result of the second relaxation of the adsorbed species involved in the different steps of the ORR. More recently, Wiezell et al.19 con-
Figure 1. Comparison of impedance data obtained for a PEM fuel cell that were determined by measurement model techniques to be consistent with the Kramers–Kronig relations.9 Symbols represent experimental data and solid lines represent the measurement model fit. The arrow points to the nominal zero-frequency impedance obtained from the slope of the polarization curve. 共a兲 Data collected at 0.2 A/cm2 using the Scribner 850C and 共b兲 data collected at 0.2 A/cm2 using Gamry FC350 impedance instrument coupled with a Dynaload RBL:100V-60A-400W electronic load.
Journal of The Electrochemical Society, 154 共12兲 B1378-B1388 共2007兲 sidered a two-step hydrogen oxidation reaction 共HOR兲 and have reported low-frequency inductive loops for impedance study in frequency range of 100 kHz–6 mHz. The work was performed for a dry system where water dynamics were expected to be more significant. They explained that the inductive loops were the result of changing factors such as water concentration, membrane thickness, hydrogen pressure, and the HOR kinetics. The influence of side reactions and reaction intermediates on the impedance response is comparatively unexplored. Side reactions and the associated intermediates can degrade fuel cell components such as membranes and electrodes, thereby reducing the lifetime, one of the crucial issues in the commercialization of fuel cells.20,21 The role of intermediates in the ORR is supported by independent observation of hydrogen peroxide formation in PEM fuel cells.22-24 A rotating-ring-disk-electrode study25 revealed that formation of the peroxide on platinum particles supported on carbon 共catalyst used in the fuel cell兲 is quite possible by two-electron reduction while the formation was not observed on clean bulk platinum. The hydrogen peroxide formed as an intermediate causes chemical degradation of the membrane.24 Other reactions have also been reported which could potentially account for the low-frequency features observed in the impedance data. Platinum dissolution, for example, has been observed in PEM fuel cells26 which can lead to the loss of catalytic activity and, consequently, to the degradation of the fuel cell performance.27 The objective of this work was to identify chemical and electrochemical reactions that could account for the low-frequency inductive impedance response and could therefore be incorporated into mechanistic models for the impedance response of PEM fuel cells. The model responses were compared to experimental results. The preliminary model development was reported in our previous work.28 Experimental
ments FC350 impedance analyzer coupled with a Dynaload electronic load RBL 100V-60A-400W. The two instruments yielded comparable levels of stochastic errors and comparable artifact-free frequency ranges.9 All electrochemical measurements were performed with a two-electrode cell in which the anode was used as a pseudo-reference electrode. The impedance measurements were conducted in galavanostatic mode for a frequency range of 1 kHz to 1 mHz with a 10 mA peak-to-peak sinusoidal perturbation. The corresponding potential perturbation ranged from 0.04 to 0.4 mV. The frequencies were spaced in logarithmic progression with 10 points per frequency decade. Impedance scans were conducted in auto-integration mode with a minimum of two cycles per frequency measured. Each scan required 5 h for the Scribner system and 3 h for the Gamry system. The difference in time required can be attributed to differences in impedance settings. Replicated impedance measurements were performed at different points on the polarization curve. Model Framework The development of impedance models for specific hypothesized reaction sequences is presented in this section. The mass-transfer problem was simplified significantly by assuming that the membrane properties were uniform, that issues associated with flooding and gas-phase transport could be neglected, and that the heterogeneous reactions took place at a plane, e.g., the interface between the catalyst active layer and the proton exchange membrane. This preliminary approach does not account for the spatial distribution of the catalyst particles in the catalyst layer, but this simplified treatment is sufficient to explore the role of specific reaction on impedance features, such as the low-frequency inductive loops. Polarization curve.— The current density can be expressed as a function of electrode potential V, concentrations of reactants ci共0兲 at electrode surface, and surface coverage ␥k as
The experimental system, impedance instrumentation, and supporting experimental techniques are presented in this section. Materials and chemicals.— The membrane electrode assembly 共MEA兲 共purchased from Ion Power, Inc., New Castle, DE兲 employed 0.0508 mm 共2 mils兲 thick Nafion N112 with catalyst layers of about 0.025 mm on both sides of the membrane. The active surface area was 5 cm2. The catalyst layers were platinum supported on carbon with a Pt catalyst loading of 0.4 mg/cm2 on both the anode and the cathode sides. The gas diffusion layer 共GDL兲 was 0.284 mm thick, made of carbon cloth. The graphite flow channel had a singlechannel horizontal serpentine flow configuration with the outlet lower than the inlet to facilitate removal of condensed water. A torque of 45 in. pounds was applied to the fuel cell assembly. Hydrogen gas was used as fuel and compressed air was used as oxidant for experiments. Compressed N2 was used to purge the fuel cell before and after experiments. A Barnstead E-Pure water system was used as a source of deionized water delivered to the anode and the cathode humidifiers. An 850C fuel-cell test station 共supplied by Scribner Associates, Southern Pines, NC兲 was used to control reactant flow rates and temperatures. The test station was connected to a computer by an interface for data acquisition. The gas flow to the anode was held at temperature of 40 ± 0.1°C, and the gas flow to the cathode was held at a temperature of 35 ± 0.1°C. The gas flows were humidified to 100% relative humidity at the respective temperatures. The cell temperature was held at 40 ± 0.1°C. The hydrogen flow rate was 0.1 L/min and the air flow rate was 0.5 L/min. The maximum stoichiometry for hydrogen and air was 1.5 and 2.5, respectively, and the cell was operated at the fully humidified condition. Electrochemical impedance measurements.— Impedance measurements were performed using two different systems. The 850°C fuel-cell test station contains both an electronic load and a frequency response analyzer. Impedance measurements obtained with the 850°C were compared to impedance collected using a Gamry Instru-
B1379
i = f共V,ci共0兲,␥k兲
关1兴
The reactants and products were assumed to diffuse through ionomer agglomerates in the catalyst layer. Concentrations of reactants and products at the reaction plane were calculated from the bulk concentrations ci共⬁兲 and the mass-transfer-limited current densities ilim using
冉
¯ci共0兲 = ci共⬁兲 1 −
¯i ilim
冊
关2兴
where ilim =
nFDici共⬁兲 ␦i
关3兴
␦i is the diffusion film thickness, F is Faraday’s constant, Di is the diffusivity of the reactant through ionomer agglomerates in the catalyst layer, and n is the number of electron exchanged in the reaction. The steady-state surface coverage was calculated by material balance of the intermediates involved in the proposed reaction mechanism. The steady-state current for each reaction was calculated as function of overpotential using the values of the steady-state surface coverage and concentrations. The total steady-state current was calculated by adding current contributions from all participating reactions at the cathode, and the total current at the anode was equated to the total current from the cathode to calculate the anode overpotential a, i.e. a =
冢
1 log b H2
¯i T,c
冉
¯i T,c KH2cH2共⬁兲 1 − ilim
冊冣
关4兴
where ¯iT,c is the total cathode current, KH2 is the rate constant for the HOR defined as in Eq. 18, cH2 is the concentration of the hydrogen,
Journal of The Electrochemical Society, 154 共12兲 B1378-B1388 共2007兲
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and bH2 is the Tafel constant for the HOR. The cell potential U was given by U = Ueq − c − 共− a兲 − IRe
关5兴
where c is the cathode overpotential and Re is the frequencyindependent ohmic resistance. Impedance response.— The faradaic current density can be expressed in terms of a steady-state contribution ¯i and an oscillating contribution ˜i as if = ¯if + Re兵i˜f exp共jt兲其
关6兴
where j = 冑−1, t is time, and is the frequency in units of s . A Taylor series expansion of Eq. 1 about the steady-state value yields −1
˜i = f
冋冏 冏 册 冋冏 冏 冋冏 冏 册 f V
+
f ci,0
˜V +
ci共0兲,␥k
f ␥k
V,ci共0兲,␥ j⫽k
V,c j⫽i共0兲,␥k
册
˜ci共0兲
˜␥k
关7兴
where ˜V, ˜ci共0兲, and ˜␥k were assumed to have small magnitudes such that the higher-order terms in the expansion can be neglected. An expression for ˜ci共0兲 was found in terms of ˜if using ˜i = nFD ci f i y or
冉
˜i ␦ 1 f i − nFDi i⬘共0兲
˜ci共0兲 =
关8兴
冊
关9兴
where i⬘共0兲 represents the dimensionless gradient of the oscillating ˜ i共0兲. Under the assumption that mass transfer concentration = ˜ci /c is through a Nernst stagnant diffusion layer −1 i⬘共0兲
=
tanh冑 jKi
冑 jKi
关10兴
Figure 2. A schematic representation of the relationship between the fuel cell geometry and an equivalent circuit diagram for proposed reaction sequences where the boxes represent faradaic impedances determined for specific reaction mechanisms.
inductive loops. model 1 incorporates a single-step ORR at the cathode and a single-step HOR at the anode. model 2 treats hydrogen peroxide formation in a two-step ORR at the cathode along with a single-step HOR at the anode, and model 3 includes the single-step ORR coupled with the platinum catalyst dissolution at the cathode along with a single-step HOR at the anode. The literature suggests that the rate should be of the order of 3/2 with respect to proton concentration and of the order of 1 with respect to the oxygen concentration.7 For the present work, the surface concentration of the proton was assumed to be constant and was therefore incorporated into the effective reaction rate constant. Model 1: Simple reaction kinetics.— The ORR O2 + 4H+ + 4e− → 2H2O
where Ki =
␦i2 Di
关11兴
The faradaic current was calculated by summing contributions from all the reactions in accordance with the reaction stoichiometry. The total current was found by summing the interfacial charging current and the faradaic current, i.e. i = if + C0
dV dt
关12兴
where C0 is the interfacial capacitance. For a small-amplitude sinusoidal perturbation, the total current was written as ˜i = ˜i + jC ˜V f 0
关13兴
An analytical expression for impedance was calculated for each model using ˜ ˜V U Z= = Re + ˜i ˜i
关14兴
was assumed to take place at the cathode. The steady-state current density expression corresponding to this reaction was assumed to be ˜i = − K ¯c 共0兲exp共− b 兲 O2 O2 O2 O2 O2
The relationship between the fuel cell geometry and an equivalent circuit diagram for proposed reaction sequences is presented in Fig. 2, where the boxes represent faradaic impedances that are to be determined for the assumed reaction mechanisms. Three impedance models were investigated for the interpretation of low-frequency
关16兴
where KO2 = nFkO2, kO2 is the rate constant, n = 4 is the number of electrons exchanged in the reaction, bk = ␣kF/RT, ␣k is the apparent transfer coefficient for reaction k, R is the universal gas constant, T is absolute temperature, ¯ci共0兲 is the concentration at electrode surface, i = V − Veq,i, i is the surface overpotential, and Veq,i is the equilibrium potential. The single-step HOR H2 → 2H+ + 2e−
关17兴
was assumed to take place at the anode. The corresponding steadystate current expression was ¯i = K ¯c 共0兲exp共b 兲 H2 H2 H2 H2 H2
关18兴
where KH2 = nFkH2, kH2 is the rate constant, and n = 2. The overall impedance was calculated as
where U is the cell potential and V is the electrode potential. Impedance Response for Proposed Reaction Mechanisms
关15兴
Z = Re +
1 1 + 共Rt,H2 + ZD,H2兲−1 + jC0,a 共Rt,O2 + ZD,O2兲−1 + jC0,c 关19兴
where C0,c is the interfacial capacitance at the cathode, C0,a is the interfacial capacitance at the anode, Rt,O2 is the charge-transfer resistance for the ORR, i.e.
Journal of The Electrochemical Society, 154 共12兲 B1378-B1388 共2007兲 Rt,O2 = 关KO2¯cO2共0兲bO2 exp共− bO2¯O2兲兴−1
B1381
关20兴
ZD,O2 is the mass-transport impedance for the ORR, i.e. ZD,O2 =
␦ O2
−1
关21兴
¯cO 共0兲bO 4FDO O ⬘ 2共0兲 2 2 2
Rt,H2 is the charge-transfer resistance for the HOR, i.e. Rt,H2 = 关KH2¯cH2共0兲bH2 exp共bH2¯H2兲兴−1
关22兴
and ZD,H2 is the mass-transport impedance for the HOR, i.e. ZD,H2 =
␦ H2
−1 ¯cH 共0兲bH 2FDH H ⬘ 共0兲 2 2 2 2
关23兴
The term −1/i⬘共0兲 was given by Eq. 10. Equation 20-23 represent lumped parameters that can be expressed in terms of parameters used to define the steady-state polarization curve. The impedance response for model 1 can be expressed as the equivalent circuit shown in Fig. 3a for the anode where Rt,H2 is given by Eq. 22 and ZD,H2 is given by Eq. 23 and in Fig. 3b for the cathode, where Rt,O2 is given by Eq. 20 and ZD,O2 is given by Eq. 21. Model 2: Hydrogen peroxide formation.— The ORR was assumed to take place in two steps in accordance to the reaction scheme as discussed in the literature.23 The first reaction O2 + 2H+ + 2e− → H2O2
关24兴
involves formation of hydrogen peroxide 共H2O2兲 which reacts further to form water, i.e. H2O2 + 2H+ + 2e− → 2H2O
关25兴
Crossover of hydrogen to the cathode is reported to facilitate the reaction of oxygen and hydrogen at the cathode, generating hydroxyl and hydroperoxyl radicals which react further to produce hydrogen peroxide at the cathode.29 The hypothesis that H2O2 may be formed at the cathode of fuel cell is supported by the results of Inaba et al.25 They reported that formation of peroxide by a twoelectron path was favored over formation of water by a four-electron path in ORR on nanoparticles of Pt supported on carbon at cathodic potential. While their work supports formation of peroxide at the cathode of the fuel cell, peroxide formation at the anode is also possible due to O2 crossover. A more inclusive impedance model could be developed by accounting for peroxide formation at the anode. The steady-state current for Reaction 24 can be expressed as ¯i = − K ¯c 共0兲共1 − ␥ O2 O2 O2 H2O2兲exp共− bO2O2兲
关26兴
where KO2 = nFkO2 with the same notation defined for model 1, n = 2, and ␥H2O2 is the fractional surface coverage of hydrogen peroxide. The current density corresponding to the Reaction 25 can be expressed as ¯i H2O2 = − KH2O2␥H2O2 exp共− bH2O2H2O2兲
Figure 3. Equivalent circuit diagrams for proposed reaction sequences where the boxes represent diffusion impedances or faradaic impedances determined for specific reaction mechanisms: 共a兲 anode for all models; 共b兲 cathode for model 1; 共c兲 cathode for model 2; and 共d兲 cathode for model 3.
关27兴
Zeff =
where KH2O2 = nF⌫kH2O2, n = 2, and ⌫ is the maximum surface coverage. The electrochemical reaction at the anode was given as Reaction 17, and the corresponding current expression was given as Eq. 18. Diffusion of peroxide away from the catalyst surface was ignored in the present work. Thus, the peroxide produced by Reaction 24 was subsequently consumed in Reaction 25 to form water. The overall impedance was calculated as Z = Re +
1 1 + jC0,a Rt,H2 + ZD,H2
Zeff +
A + jC0,c j2⌫F − B 关28兴
where
冋
1 1 − 共Rt,O2 + ZD,O2兲共1 − ¯␥H2O2兲 Rt,H2O2¯␥H2O2
⫻ and
1
+
A=
B=
冋
1 1 + Rt,O2 + ZD,O2 Rt,H2O2
冋
Rt,O2
1 1 − + ZD,O2 Rt,H2O2
册
1 1 − 共Rt,O2 + ZD,O2兲共1 − ¯␥H2O2兲 Rt,H2O2¯␥H2O2
关29兴
册 关30兴
册
关31兴
In Eq. 29, Rt,O2 is the charge-transfer resistance for the first step of the ORR, i.e.
Journal of The Electrochemical Society, 154 共12兲 B1378-B1388 共2007兲
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Rt,O2 = 关KO2¯cO2共0兲bO2共1 − ¯␥H2O2兲exp共− bO2¯O2兲兴−1
ZD,O2 is the mass-transfer impedance for the first step of the ORR, i.e. ZD,O2 =
␦ O2
−1 ¯cO 共0兲bO 2FDO O ⬘ 共0兲 2 2 2 2
关33兴
and Rt,H2O2 is the charge-transfer resistance for the second step of the ORR, i.e. Rt,H2O2 = 关KH2O2bH2O2␥H2O2 exp共− bH2O2¯H2O2兲兴−1
Keff = KPt + 共KPtO − KPt兲␥PtO
关32兴
¯i = − K ¯c 共0兲exp共− b 兲 O2 eff O2 O2 O2
关34兴
Z = Re +
¯␥H O 2 2 KO2¯cO2共0兲bO2 exp共− bO2¯O2兲
冉
冊
Zeff =
A=
冋
关36兴
It should be emphasized that ZO2 is not the sum of Rt,O2 and ZD,O2 due to the surface coverage. Similarly, ZH2O2 cannot be considered to be a frequency-independent Rt,H2O2. Model 3: Platinum dissolution.— The platinum dissolution was assumed to occur by a reaction scheme similar to that reported by Darling et al.,26 i.e., by an electrochemical reaction
PtO + 2H+ → Pt+2 + H2O
冉
关38兴
The model developed by Darling and Meyers resulted in an equilibrium oxide coverage by PtO.26 A similar reaction scheme for Pt dissolution with PtO as an intermediate at the cathodic potential of the fuel cell has also been reported by Dam and de Bruijn30 Also, Xu et al.31 have reported two schemes for Pt oxidation at the cathode, both having PtO as an intermediate. The current density corresponding to Reaction 37 was given by ¯i = K 共1 − ␥ 兲exp共b 兲 − K ␥ exp共− b 兲 Pt Pt,f PtO Pt,f Pt,f Pt,b PtO Pt,b Pt,b
1 1 1 + + Rt,O2 + ZD,O2 RPt,f RPt,b
1 1 + RPt,f RPt,b
关45兴
冊
册 关46兴
and B=
1 RPt,fbPt,f共1 − ¯␥PtO兲
+
1
关47兴
RPt,bbPt,b¯␥PtO
In Eq. 45, Rt,O2 is the charge-transfer resistance for the ORR, i.e. Rt,O2 = 关Keff¯cO2共0兲bO2 exp共− bO2¯O2兲兴−1
关48兴
ZD,O2 is the mass-transport impedance for the ORR, i.e. ZD,O2 =
关37兴
in which PtO is formed, followed by a chemical dissolution reaction
关44兴
A + jC0,c 2F共j⌫ + K3兲 + B
共KPtO − KPt兲 1 1 − − KeffbO2 RPt,fbPt,f共1 − ¯␥PtO兲 RPt,bbPt,b¯␥PtO
⫻
−1
Pt + H2O PtO + 2H+ + 2e−
1
where
Expressions for Rt,H2 and ZD,H2 were given by Eq. 22 and 23, respectively, as defined in model 1. The impedance response for model 2 can be expressed as the equivalent circuit shown in Fig. 3a for the anode and Fig. 3c for the cathode. The boxes in Fig. 3a represent a diffusion impedance corresponding to transport of hyrogen, and the boxes in Fig. 3c represent the faradaic impedances corresponding to the proposed reaction sequence. The term Zc in Fig. 2 is given by Zc =
1 + jC0,a Rt,H2 + ZD,H2
Zeff +
KO2¯cO2共0兲bO2 exp共− bO2¯O2兲 + KH2O2bH2O2 exp共− bH2O2¯H2O2兲
1 1 + Z O2 Z H2O2
1
+
关35兴
关43兴
where Keff is defined by Eq. 42. The overall impedance was calculated to be
The steady-state surface coverage of the peroxide is given as
=
关42兴
where KPt is the rate constant on a platinum site and KPtO is the rate constant on a platinum oxide site. The ORR was assumed to take place according to Reaction 15 with a steady-state current density given by
␦ O2 −1 ¯cO 共0兲bO 4FDO O ⬘ 共0兲 2 2 2 2
关49兴
RPt,f is the charge-transfer resistance for the forward reaction, i.e. RPt,f = 关KPt,fbPt,f共1 − ¯␥PtO兲exp共bPt,f¯Pt,f兲兴−1
关50兴
and RPt,b is the charge-transfer resistance for the backward reaction, i.e. RPt,b = 关KPt,bbPt,b¯␥PtO exp共− bPt,b¯Pt,b兲兴−1
关51兴
The steady-state surface coverage of the platinum oxide is given as ¯␥PtO =
KPt,fbPt,f exp共bPt,f¯Pt,f兲 KPt,bbPt,f exp共bPt,f¯Pt,f兲 + KPt,bbPt,b exp共− bPt,b¯Pt,b兲 + 2FK3
关39兴
关52兴
where KPt,f = nF⌫kPt,f, KPt,b = nFkPt,b, n = 2, ⌫ is the maximum surface coverage, and ␥PtO is the fractional surface coverage by PtO. The dissolution of PtO was assumed to occur according to
Model 3 was derived for a general expression of Keff as described in Eq. 42 but for KPtO Ⰶ KPt, the expression for Keff reduces to
rPtO = K3␥PtO
关40兴
and the corresponding material balance for the PtO was expressed as
␥PtO iPt = − rPtO ⌫ t 2F
Keff = KPt共1 − ␥PtO兲 which simplifies Eq. 46 to
冋
A= − 关41兴
The formation of the platinum oxide was proposed to have an indirect influence on the ORR at the cathode by changing the effective rate constant for the reaction. Thus
+
1 1 1 − − 共1 − ¯␥PtO兲bO2 RPt,fbPt,f共1 − ¯␥PtO兲 RPt,bbPt,b¯␥PtO 1
RPt,b
冊
and Eq. 45 to
关53兴
册冉
1 RPt,f 关54兴
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Figure 4. Electrochemical results obtained with H2 as reactant at the anode and air as oxidant at the cathode. The anode and cell temperatures were 40°C, and the cathode temperature was 35°C. 共a兲 Polarization curve and 共b兲 impedance response with current density as a parameter.
¯ O 共0兲bO exp共− bO ¯O 兲兴−1 Rt,O2 = 关KPt共1 − ¯␥PtO兲c 2 2 2 2
关55兴
Expressions for Rf,H2 and ZD,H2 were given by Eq. 22 and 23, respectively, as defined in model 1. The impedance response for model 3 can be expressed as the equivalent circuit shown in Fig. 3a for the anode and Fig. 3d for the cathode. The term Zc in Fig. 2 is given by Zc =
冉
1 1 + ZO2 ZPt
冊
−1
关56兴
As was discussed for model 2, the surface coverage of PtO influences the impedance contributions of ZO2 and ZPt. Results The experimental results of the steady-state and impedance measurements are discussed in this section and compared to the impedance response generated by the three mechanistic models discussed in previous sections. Experimental polarization and EIS results.— The polarization curve for the PEM fuel cell is presented in Fig. 4a. The cell response is strongly influenced by reaction kinetics at low current densities. The influence of the ohmic potential drop is evident at intermediate current densities, and the mass-transfer limitations are evident at large current densities. To explore the behavior of the fuel cell, the impedance was measured at several steady-state points on the polarization curve. Typical impedance spectra are presented in Fig. 4b for current densities chosen to be representative of the kinetic, ohmic, and mass-transfer controlled regions of the polarization curve. The impedance spectra have a general form consisting of one high-frequency capacitive loop and one incomplete low-frequency inductive loop. Similar inductive loops were reported by Makharia et al.6 for small current densities in which kinetic limitations dominate. The present work demonstrates that similar low-frequency inductive loops can be observed for all regions of the polarization curve. Model response analysis.— Equations 19, 28, and 44 provide mathematical expressions for the impedance response of a fuel cell associated with the reaction mechanisms described in the previous sections. These models were compared to the experimental polarization and impedance data. The method employed was to calculate the polarization curve that matched closely the experimental results and then to use the same parameters to estimate the impedance response at different currents. Direct regression was not employed as the model does not account explicitly for the nonuniform reaction rates along the length of the serpentine flow channels. Model parameters are presented in Table I. Constant values were assumed for the interfacial capacitance, ionic resistance in the catalyst layer, membrane resistance, and oxygen permeability through ionomer agglomerates in the catalyst layer. When appropriate, nu-
merical values were taken from the literature.2 The impedance response for all simulations corresponded to a frequency range of 10 kHz–0.001 mHz. Calculations at low frequency were used to explore more fully the low-frequency inductive features. Model 1.— The polarization curve generated from model 1 is compared to experimental data in Fig. 5. The parameters used to generate the polarization curve were then used to calculate the impedance response. The results for an intermediate current 共1 A or 0.2 A/cm2兲 are compared in Fig. 6 to the experimental data. The impedance response for model 1 consisted of one compressed capacitive loop with a straight-line portion at high frequency. Similar impedance spectra have been reported in the literature.5,32,33 The capacitive arc can be attributed to the single-step ORR at the cathode. The straightline portion at the higher frequencies can be attributed to mass transport impedance associated with diffusion of oxygen. Model 1 provides a reasonable representation of the capacitive loops, but cannot account for the inductive loops seen at low frequency. The inability of model 1 to account for the low-frequency inductive loops is seen more clearly in Fig. 7a and b, where the real and imaginary parts of the impedance are presented, respectively, as functions of frequency. Model 1 provided similar agreement to the experimental results at both lower and higher current densities. Thus, the model that accounts for only the hydrogen oxidation and oxygen reduction reactions cannot explain the inductive behavior at low frequencies. Models 2 and 3.— The polarization curves generated with models 2 and 3 are presented in Fig. 8. The presence of the side reactions in
Table I. Parameters used to calculate the impedance response corresponding to models 1, 2, and 3. Parameters 2
DO2, m /s DH2, m2 /s DH2O2, m2 /s ␦, m Re, ⍀ cm2 C 0, F bH2, V−1 bO2,V−1 bH2O2, V−1 bPt, V−1 KH2, A cm/mol KO2, A cm/mol KH2O2, A/mol KPt, A cm/mol KPtO, A cm/mol K3, mol/s KPt,f , A/mol KPt,b, A/cm2
Model 1
Model 2
Model 3
4 ⫻ 10 4 ⫻ 10−9 — 1 ⫻ 10−6 0.135 0.212 65 27 — — 0.55 961.9 — — — — — —
4 ⫻ 10 4 ⫻ 10−9 4 ⫻ 10−15 1 ⫻ 10−6 0.135 0.212 40 27 15 — 1.34 10,900 1900 — — — — —
4 ⫻ 10−11 4 ⫻ 10−9 — 1 ⫻ 10−6 0.135 0.212 40 45 — 14 1.35 10,900 — 6.2 0.01 0.01 0.01 0.01
−11
−11
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Figure 5. Polarization curve generated by model 1 for 40°C using parameters reported in Table I and compared with the experimental data presented in Fig. 4a.
the model has little discernable influence on the polarization curve because these reactions are assumed to be taking place at a low rate as compared to the dominant hydrogen oxidation and oxygen reduction reactions. The relative contributions of the different reactions at the cathode are shown in Fig. 9. As shown in Fig. 9a, the two reduction steps in model 2 contributed equally to the total current because the desorption/loss of peroxide was not considered in the model development. The contribution to total current by platinum dissolution shown in Fig. 9b was found to be negligible as compared to oxygen reduction. The impedance response for the model with the hydrogen peroxide formation 共model 2兲 consisted of one high-frequency capacitive loop and one low-frequency inductive loop. The impedance response for the model accounting for platinum dissolution 共model 3兲 also consisted of one high-frequency capacitive loop and one lowfrequency inductive loop. A comparison between the model and experiment is presented in Nyquist format in Fig. 10 for current densities in the kinetically controlled part of the polarization curve. The real and imaginary parts of the impedance are presented as functions of frequency in Fig. 11a and b, respectively. Similar results are shown in Fig. 12, 13a, and b for the intermediate current density and in Fig. 14, 15a, and b for high current densities. Impedance measurements are much more sensitive than polarization curves to the presence of minor reactions. Both models 2 and 3 were found to be capable of yielding low-frequency inductive loops at all portions of the polarization curve.
Figure 6. Impedance response for 0.2 A/cm2 generated by model 1 for 40°C using parameters reported in Table I and compared with the experimental data presented in Fig. 4b.
Figure 7. Impedance response for 0.2 A/cm2 generated by model 1 for 40°C using parameters reported in Table I. 共a兲 Real part of the impedance of the model response compared with the experimental data presented in the Fig. 4b and 共b兲 imaginary part of the impedance of the model response compared with the experimental data presented in Fig. 4b.
Discussion The inductive loops seen in low-frequency impedance measurements for PEM fuel cells have gained recent attention in the litera-
Figure 8. Polarization curve generated by models 2 and 3 for 40°C using parameters reported in Table I and compared with the experimental data presented in Fig. 4a.
Journal of The Electrochemical Society, 154 共12兲 B1378-B1388 共2007兲
Figure 9. Relative contributions of two reactions to total current at the cathode: 共a兲 model 2 and 共b兲 model 3.
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Figure 11. Impedance response for 0.05 A/cm2 generated by models 2 and 3 for 40°C using parameters reported in Table I. 共a兲 Real part of the impedance of the model response compared with the experimental data presented in Fig. 4b and 共b兲 imaginary part of the impedance of the model response compared with the experimental data presented in Fig. 4b.
ture. Several explanations have been proposed. Models for impedance response are not unique, and many models can lead to specific features such as the low-frequency inductive loops described in the present work. The influence of carbon monoxide poisoning on the anode kinetics has been invoked by several authors.4,34-36 The cathode kinetics were limiting in the configuration employed in the present experiments, which used a symmetric platinum loading. In addition, the anode and cathode gases used were rated ultrapure, so the influence of carbon monoxide could be excluded for the present experiments. Wiezell et al.19,37 have proposed that nonuniform water transport in the anode could lead to low-frequency inductive loops
due to the influence of water on the anode kinetics. Such an explanation does not apply for the present experiments as they were dominated by cathode kinetics. Several authors have proposed that the low-frequency inductive loops could be attributed to relaxation of adsorbed intermediates species associated with cathodic reactions.6-8 The present work shows that cathodic reactions involving formation of peroxide intermediates and reactions involving formation of PtO and subsequent
Figure 10. Impedance response for 0.05 A/cm2 generated by models 2 and 3 for 40°C using parameters reported in Table I and compared with the experimental data presented in Fig. 4b.
Figure 12. Impedance response for 0.2 A/cm2 generated by models 2 and 3 for 40°C using parameters reported in Table I and compared with the experimental data presented in Fig. 4b.
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Figure 13. Impedance response for 0.2 A/cm2 generated by models 2 and 3 for 40°C using parameters reported in Table I. 共a兲 Real part of the impedance of the model response compared with the experimental data presented in Fig. 4b and 共b兲 imaginary part of the impedance of the model response compared with the experimental data presented in Fig. 4b.
Figure 15. Impedance response for 0.3 A/cm2 generated by models 2 and 3 for 40°C using parameters reported in Table I. 共a兲 Real part of the impedance of the model response compared with the experimental data presented in Fig. 4b and 共b兲 imaginary part of the impedance of the model response compared with the experimental data presented in Fig. 4b.
dissolution of platinum can result in low-frequency inductive loops. An interesting aspect of model 3 is that the inductive loop is controlled by formation of PtO. The corresponding low-frequency inductive loops can be seen even at very low rates of Pt dissolution. These interpretations are supported by a growing number of articles in the recent literature describing evidence of peroxide formation and platinum dissolution under normal PEM operating conditions.38-44
Models based on proposed reaction hypothesis can be used to gain insight into the reaction mechanism. For example, models 2 and 3, respectively, invoked surface coverage by peroxide and PtO. The surface coverage predicted by these models is presented in Fig. 16a and b as function of potential and current density, respectively. As shown in Fig. 16a, the fractional coverage of the intermediates in both the models increased with the increase in the cell potential. The presentation in Fig. 16b as a function of current density shows that the fractional coverage of the intermediates decreases with increasing current. The models presented in the present work, while based on plausible reaction mechanisms, are ambiguous. Both the reactions involving adsorbed peroxide and formation of PtO were capable of predicting the low-frequency inductive loops observed in the impedance response of the fuel cell. This work demonstrates the need to couple the impedance measurements with supporting experiments to identify the reactions taking place within the system.45 Experimental results can be found in the literature that support both reaction mechanisms. Both the reactions involving adsorbed peroxide and formation of PtO could exist simultaneously in this system, which could account for the appearance of two time constants in the experimental low-frequency inductive loops. Conclusion
Figure 14. Impedance response for 0.3 A/cm2 generated by models 2 and 3 for 40°C using parameters reported in Table I and compared with the experimental data presented in Fig. 4b.
Low-frequency inductive loops were observed in impedance measurements of a single-cell PEM fuel cell. These loops were found to be consistent with the Kramers–Kronig relations and were observed for all parts of the polarization curve. Three analytic im-
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List of Symbols bi c C0 Di i K3 K H2
K H2O2 K O2 KPt KPt,b KPt,f KPtO n Re U Zj Zr ␦ ⌫ ␥ i
Tafel constant 共inversely related to the Tafel slope兲, V−1 concentration, mol/cm3 double layer capacitance, F/cm2 diffusivity of i species in ionomer agglomerates of the catalyst layer, m2 /s current density, mA/cm2 rate constant, mol/s rate constant of hydrogen oxidation, A cm/mol rate constant of peroxide formation, A/mol rate constant of oxygen reduction, A cm/mol rate constant of Pt oxidation, A cm/mol backward rate constant of Pt oxidation, A/cm2 forward rate constant of Pt oxidation, A/mol rate constant of PtO formation, A cm/mol number of electron exchanged in the reaction membrane resistance, ⍀ cm2 cell potential, V Imaginary part of impedance, ⍀ cm2 Real part of impedance, ⍀ cm2 diffusion layer film thickness, m maximum surface concentration, mol/cm2 fractional surface concentration, dimensionless overpotential, V frequency, s−1
References
Figure 16. Fractional surface coverage of the intermediates plotted 共a兲 as a function of cell potential and 共b兲 as a function of current density.
pedance models were derived from consideration of specific reaction sequences proposed to take place in PEM fuel cells. The model that accounted only for hydrogen oxidation and oxygen reduction could not account for the low-frequency inductive loops observed in experimental data. Models that accounted for additional reactions, i.e., formation of hydrogen peroxide and formation of PtO with subsequent dissolution of Pt, could predict low-frequency inductive loops. These models were supported by complementary experiments, and the results show that either of these reaction mechanisms could account for the experimentally observed low-frequency inductive loops. These models can also be used to predict such variables as the fractional surface coverage of the proposed intermediates. The formation of intermediates in both proposed reaction mechanisms is supported by experimental investigations available in the literature. Thus, both reaction sequences proposed in models 2 and 3 are likely in the PEM fuel cell under study, and both the reaction sequences were found to yield low-frequency inductive loops in the impedance response. Supporting experiments are required to reject or accept either of the mechanisms for the interpretation of the response. This work suggests that quantitative analysis of lowfrequency inductive loops may provide a useful characterization of reactions which reduce the efficiency and operating lifetime of PEM fuel cells. Acknowledgments This work was supported by NASA Glenn Research Center under grant no. NAG 3-2930 monitored by Timothy Smith with additional support from Gamry Instruments Inc.
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